Moderate -0.3 This is a straightforward optimization problem requiring substitution to eliminate one variable, expansion to get a quadratic in x, differentiation, and solving du/dx = 0. All steps are routine A-level techniques with no conceptual challenges, making it slightly easier than average but still requiring multiple standard procedures.
Variables \(u\), \(x\) and \(y\) are such that \(u = 2x(y - x)\) and \(x + 3y = 12\). Express \(u\) in terms of \(x\) and hence find the stationary value of \(u\). [5]
Question 4:
4 | u =2x(y−x) and x+3y =12,
12−x
u =2x −x
3
=8x−8x2
3
du 16x
=8−
dx 3
= 0 when x = 11
2
→ ( y = 31 )
2
→ u = 6 | M1 A1
M1
A1
A1
[5] | Expresses u in terms of x
Differentiate candidate’s quadratic,
sets to 0 + attempt to find x, or
other valid method
Complete method that leads to u
Co
Variables $u$, $x$ and $y$ are such that $u = 2x(y - x)$ and $x + 3y = 12$. Express $u$ in terms of $x$ and hence find the stationary value of $u$. [5]
\hfill \mbox{\textit{CAIE P1 2015 Q4 [5]}}